After some good advice I've rebuilt the mast step with a number of improvements. Previously it was too far back, it sagged to leeward as the top lashing stretched, and the step at the bottom broke (mostly due to a poor glue joint).
To fix the sagging lashing, I've built a solid mast partner that sits just under the forward beam. This also moves the mast forward to just in front of the beam. This is a far forward as the mast can go, without cutting a hole in the deck and losing the forward buoyancy tank.
I've moved the mast step to the bottom of the hull. This gives the step more leverage and reduces the loads. I wasn't sure that moving the mast forward 6" would be enough, so at the moment it's only temporary - it's not painted and only held in place with screws. Also the 'keeper' block that holds the bottom of the mast in place can be moved to adjust the mast rake. In the photo there's a bit of forward rake. If this wasn't enough I'd have to have a major rethink.
In the photo you can also see where the old mast step was, the holes in the mast partner for the beam lashing, and a plastic fitting to take the down-haul and secure the rig to the boat. The mast only has to lift an inch to come out of the mast step, so I want it held in firmly.
Lowering the mast step brought the boom unacceptably low, so I've extended the mast with a short piece of wood that fits inside the laser mast (Thanks to Rob Zabukovec for that idea!). Unfortunately I sold my lathe a couple of months ago, after not using it for years, so I made this box with pins to support the wood and shaped it with a circular saw - fine except when the blade snagged the edge of the box!
We tried all this at the weekend, and it's a huge improvement. We had a good force 4 and nothing broke, despite flying the ama at times and turning it into a submarine on the other tack. Best of all the weather-helm had gone - in fact there was a small amount of lee-helm, so I can reduce the mast rake.
Another innovation this time was adding a 3 meter long 110mm diameter drain pipe as a safety ama. I calculated that it's only 30liters of buoyancy, and when I tested it in the shallows it submerged pretty easily. However, once the water reached my waist the boat stabilised with the gunnel just out of the water, and once I stopped trying to tip it, it self-righted. I think it would stop us turning turtle but I'm not sure it'll always save us. And it looks ugly!